Find the number of terms in the given AP.

AP: 7, 10, 13, ..., 43.

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Solution

The correct option is D 13
$t_{n} = a_{1} + (n - 1) d$

where,

' $a_{1}$ ' is the first term,

'd' is the common difference,

'n' is the number of terms,

' $t_{n}$ ' is the $n^{t h}$ term.

Given, $t_{n}$ = 43, $a_{1}$ =7, $a_{2}$ = 10

d = $a_{2}$ - $a_{1}$ = 10-7 = 3
Substituting these values in the equation, we get,

$43 = 7 + (n - 1) 3$

43-7 = (n-1)3

$\Rightarrow$ 36 = (n-1)3

$\Rightarrow$ 12 = n-1
$\Rightarrow$ n =13

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